Development and Implementation of Algebraic Elimination Algorithm for the Synthesis of 5-SS Spatial Seven-bar Motion Generator

5-SS 공간 7절 운동생성기 합성을 위한 대수적 소거 알고리듬의 개발과 구현

  • Published : 2000.01.01


Dimensional synthesis of planar and spatial mechanisms mostly requires solution-finding, procedure for a system of polynomial equations. In case the system is nonlinear, numerical techniques like Newton-Raphson are often used. But there are no logical ways for finding all possible solutions in such iterative methods. In this paper, algebraic elimination is used to get all solutions for the synthesis of 5-SS spatial mechanism with seven prescribed positions. The proposed algorithm is more suitable for computer implementation and takes less time than existing one. Two numerical examples are given to demonstrate the implemented algorithm.


Motion Generation;Algebraic Elimination;Determinat;Resultant;S-S or SS link


  1. Keith Martin Briggs, doubledouble library. Available from /doubledouble.html
  2. Stephen L. Moshier, Cephes Math. Library. Available from
  3. Stephen L. Moshier, Cephes Math. Library. A vailable from
  4. Lee, U. K. and Ahn, B. E., 1993, 'A Method to Analyze The Imaginary Kingpin Axis in Multi-Link Type Suspension Systems,' SAE Paper 930262
  5. Innocenti, C., and Parenti-Castelli, V., 1993, 'Closed-Form Direct Position Analysis of a 5-5 Parallel Mechanisms,' ASME Journal of Mechanical Design, Vol. 115, pp. 515-521
  6. Raghavan, M., 1993, 'The Stewart Platform of General Geometry has 40 Configurations,' ASME Journal of Mechanical Design, Vol. 115, pp. 277-282
  7. Wampler, C. W., Morgan, A. P., and Sommese, A. J., 1990, 'Numerical Computation Methods for Solving Polynomial Systems Arising in Kinematics,' ASME Journal of Mechanical Design, Vol. 112, pp. 59-68
  8. Innocenti, C., 1994, 'Polynomial Solution of the Spatial Burmester Problems,' Proceedings of the 23rd ASME Mechanisms Conference, DE-Vol. 70, pp. 161-166
  9. Erdman, A.G., and Sander G.N., 1991, Mechanism Design: Analysis and Synthesis, Prentice-Hall, Vol.1, 2nd ed., pp.635-639
  10. Boehm, W., and Prautzsch, H., 1994, Geometric Concepts for Geometric Design, A K Peters Wellesley, Massachusetts, pp. 327-335. 291-296
  12. Morgan, A. P., and Wampler, C. W., 1990, 'Solving a Planar Four-Bar Design Problem Using Continuation,' ASME Journal of Mechanical Design, Vol. 112, No.4, pp. 544-550
  13. 이태영, 심재경, 1996, '기어 5절 함수발생장치와 4절 링크 경로발생장의 설계,' 대한기계학회 추계학술대회 논문집A, pp. 954-961
  14. Raghavan, M., and Roth, B., 1995, 'Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot manipulator,' ASME Journal of Mechanical Design, Vol. 117, pp. 71-79
  15. Erdman, A. G., ed., 1993, Modern Kinematics : Developments in the Last forty Years, New York, John wiley & Sons, Inc., pp. 451-470